We are coming into Vevey to stay for the night but the next day would like to purchase either the 3 or 4 day Swiss Pass to go to the castle and then travel by train to Lauterbrunnen. Is there a place in Vevey to buy the Swiss Pass or can we purchase it at the castle?

You wouldn't be able to purchase a Swiss Travel Pass at Chillon Castle no. The most convenient option would be to buy the Swiss Travel Pass online. It gets emailed to you so you can print it out at home. This way you have it on you and there is no need to go to a rail station to buy it (and you have an electronic backup).

No, with a Swiss Travel Pass you won't need to buy a ticket for the Golden Pass route. Reservations are possible on all sections except between Zweisimmen and Montreux (which has the panorama train) due to construction. There is a small section of the route (about 10km) where you are transferred onto buses.